Methods for Probabilistic Analysis of Noncoherent Fault Trees

Four methods for the probabilistic analysis of s-coherent fault trees are investigated concerning their applicability to noncoherent fault trees. The inclusion-exclusion and min-max bounds can be extended to noncoherent fault trees, while the minimal cut (path) set bounds cannot. When a fault tree is modularized, the application of the min-max bounds or the inclusion-exclusion upper bound to both the modules and the organizing structure function yields the same bounds that are obtained without modular decomposition. If the organizing structure function or the modules are simple enough, exact calculations can be performed at either level to give an improved bound.